What is bilateral CVA (BCVA) and how does DVA fit in?

Question

AcadiFi · Accepted Answer

Bilateral CVA recognizes that BOTH parties can default. For Calder Financial trading with Northbridge:

BCVA = UCVA_Calder − DVA_Calder

Where:
- UCVA_Calder = LGD_NB × Σ[EE × PD_NB × DF] — loss if Northbridge defaults when it owes Calder
- DVA_Calder = LGD_CF × Σ[NEE × PD_CF × DF] — benefit if Calder defaults when Calder owes Northbridge

DVA (Debit Valuation Adjustment) reflects the gain a bank recognizes when its OWN credit deteriorates. NEE (Negative Expected Exposure) is E[Max(-MtM, 0)] — the expected amount the bank owes. As the bank's CDS spread widens, the present value of its own liabilities falls, creating accounting income.

Example: Calder Financial has 1Y CDS spread of 80 bps; Northbridge has 150 bps. On a swap:
- UCVA = $520K (Calder's charge for Northbridge's default risk)
- DVA = $280K (Calder's credit for its own default risk)
- BCVA = $520K − $280K = $240K net charge against MtM

Key FRM controversies:

1. **Pro-DVA argument** — symmetric accounting; if Northbridge books CVA against Calder, Calder should book DVA to balance.
2. **Anti-DVA argument** — you can't hedge your own default; DVA gains are paper gains that disappear if you survive.
3. **Regulatory treatment** — Basel excludes DVA from CET1 capital (Article 33 CRR) because it's not realizable.
4. **Accounting (IFRS 13, ASC 820)** — requires DVA in fair value; large banks report billions of DVA swings when spreads move.

For FRM, memorize: UCVA is always positive (a charge), DVA is also a positive number conceptually but enters BCVA with a minus sign. When your own CDS widens, DVA grows, reducing BCVA and creating accounting P&L.

What is bilateral CVA (BCVA) and how does DVA fit in?

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